United are in the market for another forward to boost their attacking options and looked likely to bring in Pedro until the player signed for Chelsea at the 11th hour.
Although very different types of player, United have a long-standing interest in Muller, having failed to sign him both last summer and this, with Karl-Heinz Rummenigge insisting earlier this month that the player was not for sale.
But Louis van Gaal is reportedly refusing to take no for an answer and remains keen to reunite with a player he nurtured in Germany during his time in charge of Bayern.
German tabloid Bild reported on Wednesday morning United had offered £60m for Muller, 25, in an attempt to bolster their forward line.
But with that bid again being snubbed, it’s being reported that United will offer £71million (100million euros) to persuade Bayern to sell their man.
Muller would represent a marquee addition for United, though the World Cup winner was stunned by reports of his latest ‘valuation’.
“It’s basically crazy the numbers which are currently kicking around in football – that’s just business,” Muller told German broadcaster Sport1.
“No one is €100m, it’s just a trade figure, so I am quite relaxed about the whole thing.”
Muller also saw the funny side of the endless speculation when he played in a testimonial match against Dynamo Dresden recently.
“In Dresden, a fan addressed me with a megaphone: ‘Hey €100m man, what is your playing shirt worth?’ That made me smile,” Muller added.
Bayern sporting executive Matthias Sammer indicated Muller would remain at the club after his two-goal weekend appearance against Hamburg.
“His performances have caused a stir, not Thomas,” Sammer said.
“We can’t be blamed for anything but this. Rummenigge was right when pointing out that he is a player who has no price tag.”